Improvement of Buckley-Leverett equation and its solution for gas displacement with viscous fingering and gravity effects at constant pressure for inclined stratified heterogeneous reservoir

Abstract

The paper presents an analytical solution of Buckley-Leverett (BL) equation in gas displacement process including viscous fingering and gravity effects at constant pressure boundary conditions for the inclined stratified heterogeneous reservoir. First, the governing equations related to the change of fluid properties, which govern viscous fingering are discussed. Then the gas flood BL-equation accounting for gravity and miscibility effects for inclined stratified heterogamous reservoir are developed and solved analytically using fractional-flow theory and MOC (method of characteristics). The analytical solution provides the guidance to predict the oil recovery through pressure and saturation distribution at any given time for horizontal, inclined, homogeneous and heterogeneous reservoirs. The results of the analytical solution (total volumetric flux, breakthrough time, front location, saturation and pressure) are compared with finite-difference numerical simulation using CMG simulator. The comparison shows that the analytical solution gives approximately similar results as finite difference numerical simulation. The results of analytical solution show that the total volumetric flux increases with increase of permeability, permeability heterogeneity, injection gas viscosity, mixing parameter and injection pressure, while it decreases with increase in gravity, reservoir inclination and normalized gas formation capacity. The breakthrough time and advance distance are found to be strong function of permeability heterogeneity, injected gas viscosity, mixing parameter and reservoir inclination angle, gravity number, normalized gas formation capacity and injection pressure. Furthermore, with increase of mixing parameter/injection pressure and decrease of permeability heterogeneity results in remarkable improvement of relative permeability and reduction of residual oil saturation led to higher oil displacement efficiency.